# Re: Idempotence and "Replication Insensitivity" are equivalent ?

Date: 24 Sep 2006 08:05:29 -0700

Message-ID: <1159110329.121576.95730_at_h48g2000cwc.googlegroups.com>

Marshall wrote:

> Aloha Kakuikanu wrote:

*> > pamelafluente_at_libero.it wrote:
**> > > The median, like the mean IS an aggregate function.
**> > >
**> > > All dbms implements it.
**> >
**> > Look up any math book. Do you see an aggregate symbol except:
**> >
**> > i. sigma capital (aka summation)
**> > ii. pi capital (aka product)
**> > iii. /\ (aka min, aka conjunction, aka "for any" quantifier)
**> > iv. \/ (aka max, disjunction, "forall" )
**> >
**> > ? I don't.
**>
**> Most of that I get, but I don't see how min and max fit in.
**> How is min related to conjunction? How is max related
**> to disjunction?
*

Lets's talk about binary operations first. Conjunction and min are the same operations. Likewise disjunction and max. They obey the same set of lattice laws. Min and max are defined on numbers: integers, reals, etc. Conjunction and disjunction is defined on boolean algebras.

When writing /\(capital) and \/(capital) I referred to n-ary (or aggregate) variants of conjunction and disjunction which are more commonly known in logic as existential and universal predicates. Received on Sun Sep 24 2006 - 17:05:29 CEST